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Update of ILC Tracker Alignment Based on Frequency Scanned Interferometry University of Michigan ILC Group (Hai-Jun Yang, Alexander Harvey Nitz, Eui Min Jung, Keith Riles) ALCPG Workshop, Fermilab October 22-26, 2007

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- FSI for ILC Tracker Alignment2 Outline Brief reminder of Frequency Scanned Interferometry (FSI) method Review of improvements & measurements of FSI demonstration system Implementation of dual-laser technique Results of measurements – estimated precision Cross checks Preliminary simulation results: Impact of silicon ladder distortion on charged track momentum reconstruction Ongoing work Miniaturization Multiple channels Detailed simulation based on FSI line-of-sight grid constraint

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- FSI for ILC Tracker Alignment3 Overview of FSI Method Measure hundreds of absolute point-to-point distances of tracker elements in 3 dimensions by using an array of optical beams split from a central laser. Absolute distances are determined by scanning the laser frequency and counting interference fringes. Grid of reference points overdetermined Infer tracker distortions Technique pioneered by Oxford U. group for ATLAS SCT detector

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- FSI for ILC Tracker Alignment4 A Possible SiD Tracker Alignment 752 point-to-point distance measurements ( Goal: σ distance < 1 μm )

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- FSI for ILC Tracker Alignment5 Principle of Distance Measurement The measured distance can be expressed by + constant end corrections c - speed of light, N – No. of fringes, - scanned frequency n g – average refractive index of ambient atmosphere Assuming the error of refractive index is small, the measured precision is given by: ( R / R) 2 = ( N / N) 2 + ( v / ) 2 Example: R = 1.0 m, = 6.6 THz, N ~ 2R /c = To obtain R 1.0 m, Requirements: N ~ 0.02, v ~ 3 MHz

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- FSI for ILC Tracker Alignment6 Background Previous reports: FSI I – Single-laser demonstration with air transport of beam FSI II – Single-laser measurements with fiber transport Results published in Applied Optics, 44, (2005) Results (~ 50 nm) well within desired precision, but only for well controlled laboratory conditions FSI III – Dual-laser measurements with fiber transport Results published in Nucl. Inst. & Meth. A575, 395(2007) More realistic detector conditions (~ 200 nm)

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- FSI for ILC Tracker Alignment7 Measured Distances: 10 cm – 60 cm Distance Precision : ~ 50 nm by using multiple-distance measurement technique under well controlled laboratory conditions. Vibration Measurement: Hz, amplitude as low as few nanometers, can be extracted precisely using new vibration extraction technique. Publication: “High-precision absolute distance and vibration measurement with frequency scanned interferometry”, [Physics/ ] H.J. Yang, J. Deibel, S. Nyberg, K. Riles, Applied Optics, 44, , (2005) Background Controlled Conditions

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- FSI for ILC Tracker Alignment8 “Real World” Cannot count on precisely controlled conditions in ILC detector tracker. Thermal fluctuations and drifts likely Refraction index and inferred distance affected Can measure temperature, pressure, humidity, etc. and apply empirical formulae, but preferable to measure effects directly and cancel these effects Use dual-laser technique (Invented by Oxford ATLAS group): Two independent lasers alternately chopped Frequency scanning over same range but with opposite slope

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- FSI for ILC Tracker Alignment9 Dual-Laser FSI (III) Two Lasers Two Choppers A dual-laser FSI (Oxford ATLAS method) has been implemented with optical choppers. Laser #1: D 1 = D true + Ω 1 1 Laser #2: D 2 = D true + Ω 2 2 Drift errors: 1 2 = D true = (D 2 - D 1 ) / (1 - ), Where = Ω 2 / Ω 1

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- FSI for ILC Tracker Alignment10 Fringes & F-P Peaks (dual-laser) Laser-1 Laser-2 Chopper edge effects and low photodiode duty cycle per laser complicate measurement.

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- FSI for ILC Tracker Alignment11 Distance Measurement Precision Distance Measurement Precision (~ cm) Laser #1 or #2 only : Precision (RMS) = 3 ~ 7 microns Combining multi-distance-measurement and dual-laser scanning techniques to reduce and cancel interference fringe uncertainties, vibration and drift errors Dual-laser precision (RMS) ~ 0.20 microns under realistic conditions A 2nd report: “High-precision absolute distance measurement using dual-laser frequency scanned interferometry under realistic conditions”, [Physics/ ], Nucl. Inst. & Meth. A575, 395(2007)

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- FSI for ILC Tracker Alignment12 FSI Cross Checks Used a Micrometer to change the position of retroreflector by large amount (127+/- 3 microns), and check FSI performance. The measurement precision is ~ 0.5 microns with unstable temperature. Used a Piezoelectric transducer (PZT, 20% tolerance) to change the position of the retroreflector by 2.0 +/- 0.4 microns. The measurement precision is ~ 0.1 microns with stable temperature. To verify correct tracking of large thermal drifts, we placed a heating pad on a 1’ x 2’ x 0.5’’ Al breadboard to increase temperature by 4 ~ 7 o C. The measured thermal expansions agree well with expectations, the measurement precision is ~ 0.2 microns.

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- FSI for ILC Tracker Alignment13 Miniaturization Previously used large commercial optics: Retroreflector (Diameter ~ 1’’) Beam splitter (Diameter ~ 1’’) Need miniaturized, low-X 0 components for actual tracker Obtained customized fabrication quotes for retroreflectors (3~4 mm) from rapid prototyping companies.

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- FSI for ILC Tracker Alignment14 Miniaturization Cheap prototype alternatives: a bicycle reflector: (all but one pixel masked off) Measurement precision for a distance of 18 cm: ~ 0.4 μm Promising indication, given simple design of the reflector pixels ( solid plastic corner cubes with no coating, but low reflective efficiency )

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- FSI for ILC Tracker Alignment15 Miniaturization Now using Edmund corner cube array, 9 X 9 hexagon corner cubes in 35 mm X 35 mm. Center-to-center spacing of two adjacent corner cubes is ~ 4 mm. The reflective efficiency of single corner cube is comparable to large commercial corner cube and hollow retroreflector ( D = 1 inch ). High reflective efficiency is vital to make qualified fringes and to make more channels. Under controlled conditions L = / microns The corner cube array has high reflective efficiency and qualified fringes. It’s very promising.

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- FSI for ILC Tracker Alignment16 We are implementing multi-channels fed by an optical fiber splitter Double-check systematics Implement multiple distance measurements and test over- constrained algorithm for a prototype set of reference points Preparation for test of silicon ladder prototype alignment Multiple channels Results not ready yet !

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- FSI for ILC Tracker Alignment17 Simulation To evaluate the impact of distortion of silicon ladder on charged track momentum reconstruction/measurement. Integrated track generation, reconstruction and FSI fitting Inputs: charged track with given momentum, 5 silicon layers based on nominal SiD design, magnetic field B = 5 Tesla. -- Assume spatial resolution is 7 microns for hits. -- Distortions: rotations, translations, thermal expansion or contractions of silicon ladders. -- Applying FSI line-of-sight grid constraint (code not fully debugged – premature to show results, but consistent with earlier simulations.) Outputs: reconstructed momentum of charged track, event displays for SiD Tracker

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- FSI for ILC Tracker Alignment18 Example Tracks (side view) Can zoom in on specific locations

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- FSI for ILC Tracker Alignment19 Normal ( = 7 microns for hits) P true = 100 GeV, hit smearing ~ 7 microns P rec -P true (GeV)

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- FSI for ILC Tracker Alignment20 Normal ( = 20 microns for hits) P true = 100 GeV, hit smearing ~ 20 microns P rec -P true (GeV)

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- FSI for ILC Tracker Alignment21 Translation of Silicon Ladder (Middle) P true = 100 GeV, shift ~ 1 micron P rec -P true (GeV)

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- FSI for ILC Tracker Alignment22 Translation of Silicon Ladder (Middle) P true = 100 GeV, shift ~ 10 microns P rec -P true (GeV)

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- FSI for ILC Tracker Alignment23 Translation of Silicon Ladder (Middle) P true = 100 GeV, shift ~ 100 microns P rec -P true (GeV)

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- FSI for ILC Tracker Alignment24 Translation of Silicon Ladder (Middle) P true = 100 GeV, shift ~ microns P rec -P true (GeV)

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- FSI for ILC Tracker Alignment25 Rotation of Silicon Ladder (Middle) P true = 100 GeV, Rotate ~ 1*10 -6 rad P rec -P true (GeV)

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- FSI for ILC Tracker Alignment26 Rotation of Silicon Ladder (Middle) P true = 100 GeV, Rotate ~ 1*10 -5 rad P rec -P true (GeV)

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- FSI for ILC Tracker Alignment27 Rotation of Silicon Ladder (Middle) P true = 100 GeV, Rotate ~ 1*10 -4 rad P rec -P true (GeV)

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- FSI for ILC Tracker Alignment28 Summary Several FSI demonstration systems with increasing realism have been implemented Results on achievable measurement precision are quite promising (~ 0.2 microns with dual-laser scanning) Published Results Hai-Jun Yang, Sven Nyberg, Keith Riles, " High-precision Absolute Distance Measurement using Dual-Laser Frequency Scanned Interferometry Under Realistic Conditions ", Nucl. Instrum. & Meth. A575 (2007) Nucl. Instrum. & Meth. A575 (2007) Hai-Jun Yang, Jason Deibel, Sven Nyberg, Keith Riles, " High-precision absolute distance and vibration measurement using frequency scanned interferometry", Applied Optics, Vol.44 (2005) Applied Optics, Vol.44 (2005)

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- FSI for ILC Tracker Alignment29 Summary Ongoing work: Miniaturization: baseline retroreflector is plexiglass, but want to investigate other materials (constrained by available prototyping funds) Multiple channels: dual-channel system nearly ready Simulations: integrated framework nearly complete, early results seem promising

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- FSI for ILC Tracker Alignment30 Backup Slides

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- FSI for ILC Tracker Alignment31 Fringe Interpolating Technique 5 FSRs Fringe phase = I+ IFringe phase = J+ J Fringe correction (N_corr) must satisfy: minimize | N_corr+(J+ J)-(I+ I)-N_average | Where, N_corr is integer number, N_average is expected average fringe numbers (real) for the given number of FSRs. Expected fringes for 5 FSRs Laser #1 data with chopperLaser #1 data without chopper

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- FSI for ILC Tracker Alignment32 Distance Measurement Precision Dual-Laser FSI Data Samples – Under Realistic Conditions * with box open(20 scans), with fan on (10 scans), with vibration(8 scans). * Scanning rates for Laser #1 and #2 are -0.4 and 0.4 nm/s, respectively. * Scanning time is 25 seconds, sampling rate is 100 KS/s. * Two lasers are operated simultaneously, 2-blade chopper frequency is 20 Hz.

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- FSI for ILC Tracker Alignment33 FSI Cross Checks Used a Micrometer to change the position of retroreflector by large amount (127+/- 3 microns), and check FSI performance. Laser #1, 5 full scan data for each independent test. dR1 = / microns dR2 = / microns dR3 = / microns dR4 = / microns Used a Piezoelectric transducer (PZT, 20% tolerance) to change the position of the retroreflector by 2.0 +/- 0.4 microns. Laser #1, 5 full scans for each test. dR5 = / microns dR6 = / microns Single-laser scans – unstable temps Single-laser scans – stable temps

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- FSI for ILC Tracker Alignment34 FSI Thermal Test To verify correct tracking of large thermal drifts, we placed a heating pad on a 1’ X 2’ X 0.5’’ Aluminum breadboard Test 1: increased temperature by 6.7 +/- 0.1 o C dR_expected = /- 0.9 microns dR_measured = / microns Test 2: increased temperature by 6.9 +/- 0.1 o C dR_expected = /- 0.9 microns dR_measured = / microns Test 3: increased temperature by 4.3 +/- 0.1 o C dR_expected = /- 0.9 microns dR_measured = / microns Test 4: increased temperature by 4.4 +/- 0.1 o C dR_expected = /- 0.9 microns dR_measured = / microns Dual-laser scans closed box

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